7. Modeling with Exponential and Logarithmic Functions
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Begin by creating a table of data pairs (x,ln y) using the given information. Then, make the scatter plot of the resulting ordered pairs.
Possible Model: y=14.73(1.03)^x
We will first create a table of data pairs (x,ln y) using the given table.
x | -13 | -6 | 1 | 8 | 15 |
---|---|---|---|---|---|
y | 9.8 | 12.2 | 15.2 | 19 | 23.8 |
ln y | 2.28 | 2.50 | 2.72 | 2.94 | 3.17 |
Next, we will plot the transformed points.
Substitute ( 1,2.72) & ( 8,2.94)
Subtract terms
Calculate quotient
Round to 2 decimal place(s)
Distribute 0.03
LHS+2.72=RHS+2.72
e^(LHS)=e^(RHS)
a = e^(ln(a))
a^(m+n)=a^m*a^n
(a^m)^n=a^(m* n)
Calculate power
Multiply
Round to 2 decimal place(s)